Advanced Scale-Propeller Design Using a MATLAB Optimization Code
Abstract
:Featured Application
Abstract
1. Introduction
1.1. Rationale
1.2. Propeller Data Analysis
1.3. Aim of the Study
1.4. Literature Review
- The rotor is modelled as an actuator disk, which adds momentum and energy to the air;
- There is no inflow or outflow through the wake boundary;
- The flow is steady, incompressible and inviscid;
- The flow is one dimensional and uniform;
- The flow is uniform through the disk and wake;
- The disc does not impart any swirl to the flow.
1.5. Historical Perspective
1.6. The Optimum Propeller
2. Materials and Methods
2.1. Propeller Theory—Geometry
2.1.1. Airfoil Geometry
2.1.2. Propeller Geometry
2.2. Non-Dimensional Coefficients
2.3. Propeller/Rotor Efficiency
2.3.1. Figure of Merit
2.3.2. Propulsive Efficiency
2.4. Reynolds Number
2.5. Propeller Geometry Optimization
2.6. Calculating Propeller Geometry
2.7. Optimising Propeller Geometry
3. Results
3.1. Implementing the Optimization Method Using MATLAB
3.2. Reynolds Number Distribution
3.3. Program User Interface Design
3.4. Validation of the MATLAB Program
4. Discussion
4.1. Summary
4.2. Recommendations for Further Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
A | Propeller disc area (m2) |
B | Number of propeller blades |
c | Blade chord length (m) |
D | Propeller diameter (inches) |
F | Prandtl’s momentum loss factor |
G | Circulation function |
I1 | Thrust loading integral |
I2 | Thrust loading integral |
J | Propeller advance ratio, V/n D |
J1 | Power Loading integral |
J2 | Power Loading integral |
n | Number of complete revolutions per second |
p | Propeller pitch (inches) |
P | Shaft power consumed by propeller (W) |
Q | Propeller shaft torque (Nm) |
r | Distance along the propeller radius (m) |
R | Propeller blade radius (m) |
T | Thrust produced by the propeller (N) |
V | Freestream velocity (m/s) |
V1 | Displacement velocity (m/s) |
W | Total local velocity (m/s) |
cD | Airfoil section coefficient of drag |
cL | Airfoil section coefficient of lift |
CT | Thrust Coefficient |
CP | Power Coefficient |
CQ | Torque Coefficient |
mblade | Mass of a propeller blade (kg) |
Pc | Design Power Coefficient |
Tc | Design Thrust Coefficient |
v, | Displacement velocity (m/s) |
waxial | Induced axial velocity component (m/s) |
wswirl | Induced swirl velocity component (m/s) |
xblade | Extension of a propeller blade (m) |
xCoG | Distance from centre of rotation to propeller blade centre of gravity (m) |
Re | Reynolds number |
Greek Symbols
α | Propeller blade angle of attack (degree) |
β | Propeller blade angle of twist (degree) |
ζ | Displacement velocity ratio, v1/V |
ηp | Propeller efficiency, Tc/Pc ≡ J CT/CP |
µ | Viscosity of air (kgm−1 s−1) |
ξ | Non-dimensional radius, r/R |
Γ | Circulation (m2/s) |
ρ | Air density (kgm−3) |
σ | Rotor solidity |
Ω | Propeller angular speed (rad/s) |
φ | Flow angle (degree) |
φs | Wake helix angle (degree) |
φt | Flow angle at propeller blade tip (degree) |
Appendix A. MATLAB Program Code
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Propeller | Rotor | ||
---|---|---|---|
CTp | Propeller Thrust Coefficient | CT | Rotor Thrust Coefficient |
CPp | Propeller Power Coefficient | CP | Rotor Power Coefficient |
CQp | Propeller Torque Coefficient | CQ | Rotor Torque Coefficient |
Input | Unit |
---|---|
Diameter (D) | Inch |
Velocity (V) | m/s |
Shaft Power (P) | W |
Propeller Speed | RPM |
Air Density (ρ) | kgm−3 |
Number of Blades (B) | - |
Airfoil CL | - |
Airfoil CD | - |
Non-Dimensional Hub Radius | - |
Angle of Attack (α) | Degree |
Displacement velocity ratio convergence level | - |
Number of blade elements | - |
Input | Input Value |
---|---|
Diameter (D) | 10 inch |
Velocity (V) | 15.87 m/s |
Shaft Power (P) | 68.77 W |
Propeller Speed (n × 60) | 6519 RPM |
Air Density (ρ) | 1.225 kgm−3 |
Number of Blades (B) | 2 |
Airfoil CL | 0.4 |
Airfoil CD | 0.02 |
Non-Dimensional Hub Radius | 0.15 |
Angle of Attack (α) | 0◦ |
Displacement velocity ratio convergence level | 0.1 |
Number of blade elements | 100 |
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Prior, S.D.; Newman-Sanders, D. Advanced Scale-Propeller Design Using a MATLAB Optimization Code. Appl. Sci. 2024, 14, 6296. https://doi.org/10.3390/app14146296
Prior SD, Newman-Sanders D. Advanced Scale-Propeller Design Using a MATLAB Optimization Code. Applied Sciences. 2024; 14(14):6296. https://doi.org/10.3390/app14146296
Chicago/Turabian StylePrior, Stephen D., and Daniel Newman-Sanders. 2024. "Advanced Scale-Propeller Design Using a MATLAB Optimization Code" Applied Sciences 14, no. 14: 6296. https://doi.org/10.3390/app14146296
APA StylePrior, S. D., & Newman-Sanders, D. (2024). Advanced Scale-Propeller Design Using a MATLAB Optimization Code. Applied Sciences, 14(14), 6296. https://doi.org/10.3390/app14146296